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Regression Analysis with MATLAB. MATLAB codes Read the data into workspace of MATLAB clear; data=xlsread('D:\UIC lectures\RA 2010\chap3\hospital manpower.xls');

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Presentation on theme: "Regression Analysis with MATLAB. MATLAB codes Read the data into workspace of MATLAB clear; data=xlsread('D:\UIC lectures\RA 2010\chap3\hospital manpower.xls');"— Presentation transcript:

1 Regression Analysis with MATLAB

2 MATLAB codes Read the data into workspace of MATLAB clear; data=xlsread('D:\UIC lectures\RA 2010\chap3\hospital manpower.xls');

3 MATLAB codes

4 Read the data into workspace of MATLAB y=data(:,3); x(:,2)=data(:,2); x(:,1)=1; n=size(x,1);

5 MATLAB codes Read the data into workspace of MATLAB

6 MATLAB codes Computation steps

7 MATLAB codes Calculate Beta and Q beta=inv(x'*x)*x'*y; Q=(y-x*beta)'*(y-x*beta);

8 MATLAB codes Calculate Beta and Q

9 MATLAB codes Calculate H, yhat, sigma square and covariance of beta h=x*inv((x'*x))*x'; yhat=h*y; sigma2=Q/(n-2); covbeta=sigma2*inv(x'*x);

10 MATLAB codes Calculate H, yhat, sigma square and covariance of beta

11 MATLAB codes Calculate H, yhat, sigma square and covariance of beta

12 MATLAB codes Define Dn yi=ones(n,1); i=eye(n); D=i-(1/n)*yi*yi';

13 MATLAB codes Define Dn

14 MATLAB codes Compute SStotal and SSreg SStotal=y'*D*y; SSreg=yhat'*D*yhat;

15 MATLAB codes Compute SStotal and SSreg

16 ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 Residual0.863 Total111.917

17 ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917

18 ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 N=? Sigma square=? R square=?

19 ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 N=12 Sigma square= 0.0863 R square=0.550

20 ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 b1=? b0=? Var(b1)=? Var(b0)=? X bar=49.3333 Y bar=3.5 Sxx=306.67 Sxy=17.97

21 ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 b1=0.059 b0=0.003 Var(b1)= 0.000281 Var(b0)= 0.69208 X bar=49.3333 Ybar=3.5 Sxx=306.67 Sxy=17.97

22 ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 t(b1)=? X bar=49.3333 Ybar=3.5 Sxx=306.67 Sxy=17.97

23 ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 t=3.493 X bar=49.3333 Ybar=3.5 Sxx=306.67 Sxy=17.97

24 ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 Var(y-hat)=?, at x=45 X bar=49.3333 Ybar=3.5 Sxx=306.67 Sxy=17.97

25 ANOVA table Class exercises Source Degrees of Freedom Sum of Squares Mean Squares F Regression11.053 12.202 Residual100.8630.0863 Total111.917 Var(y-hat)=0.012476, at x=45 X bar=49.3333 Ybar=3.5 Sxx=306.67 Sxy=17.97

26 That’s all


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